Concept

Convex polytope

Related publications (143)

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Convex Variational Bayesian Inference for Large Scale Generalized Linear Models

Matthias Seeger

We show how variational Bayesian inference can be implemented for very large binary classification generalized linear models. Our relaxation is shown to be a convex problem for any log-concave model, and we provide an efficient double loop algorithm for so ...

2009

Convexly independent subsets of the Minkowski sum of planar point sets

János Pach, Friedrich Eisenbrand, Thomas Rothvoss

Let P and Q be finite sets of points in the plane. In this note we consider the largest cardinality of a subset of the Minkowski sum S ⊆ P⊕Q which consist of convex independent points. We show that, if P and Q contain at most n points, then |S| = O(n^(4/3) ...

American Mathematical Society2008

Points surrounding the origin

János Pach, Andreas Fukami Holmsen

Suppose d > 2, n > d+1, and we have a set P of n points in d-dimensional Euclidean space. Then P contains a subset Q of d points such that for any p ∈ P, the convex hull of Q∪{p} does not contain the origin in its interior. We also show that for non-emp ...

2008

Characterization of equilibrium measures for critical reversible Nearest Particle Systems

We show that for critical reversible attractive Nearest Particle Systems all equilibrium measures are convex combinations of the upper invariant equilibrium measure and the point mass at all zeros, provided the underlying renewal sequence possesses moments ...

2008

Parametric B-Spline Snakes on Distance Maps—Application to Segmentation of Histology Images

Michaël Unser, Philippe Thévenaz, François Aguet, Chandra Sekhar Seelamantula

We construct parametric active contours (snakes) for outlining cells in histology images. These snakes are defined in terms of cubic B-spline basis functions. We use a steerable ridge detector for obtaining a reliable map of the cell boundaries. Using the ...

EURASIP2008

Fixed-Order Controller Design for Systems with Polytopic Uncertainty Using LMIs

Alireza Karimi, Roland Longchamp, Hamid Khatibi

Convex parameterization of fixed-order robust stabilizing controllers for systems with polytopic uncertainty is represented as an LMI using KYP Lemma. This parameterization is a convex inner-approximation of the whole non- convex set of stabilizing control ...

2008

Symmetry breaking in a plasmonic metamaterial - art. no. 698715

Olivier Martin

We numerically study the optical properties of metal lattices made from periodically arranged plasmonic molecules, i.e., coupled gold nanowire pairs. It is shown that the interaction between the metallic wires, which is directly controlled by the specific ...

Spie-Int Soc Optical Engineering, Po Box 10, Bellingham, Wa 98227-0010 Usa2008

0/1 vertex and facet enumeration with BDDs

Friedrich Eisenbrand

In polyhedral studies of 0/1 polytopes two prominent problems exist. One is the vertex enumeration problem: Given a system of inequalities, enumerate its feasible 0/1 points. Another one is the convex hull problem: Given a set of 0/1 points in dimension d, ...

2007

f-vectors of Minkowski additions of convex polytopes

Christophe Weibel

The objective of this paper is to present two types of results on Minkowski sums of convex polytopes. The first is about a special class of polytopes we call perfectly centered and the combinatorial properties of the Minkowski sum with their own dual. In p ...

2007

Minkowski sums of polytopes

Christophe Weibel

Minkowski sums are a very simple geometrical operation, with applications in many different fields. In particular, Minkowski sums of polytopes have shown to be of interest to both industry and the academic world. This thesis presents a study of these sums, ...

EPFL2007